Using coordinates rule of Dilation , The ratio (new to original) of perimeter is 1/√2
The ratio of (new to original) of area is ½
The coordinates of the vertices of Square are (0,0),(0,4),(4,0) and (4,4).
Let the vertices be
A(0,0),B(0,4),C(4,0),D(4,4) of square ABCD. Also , scaling factor k= 0.5 or ½ .
Now, we shall find out the coordinates of square KLMN which is image of Square ABCD.
Use the coordinates rule for dilation with k= ½
(x,y) → (kx , ky)
(kx , ky ) represents coordinates of new square KLMN.
(0,0) →(0,0)=K(0,0)
(0,4)→ ( 0×(1/2), 4(1/2))= L(0,2)
(4,0)→( 4(1/2), 0(1/2)) = M(2,0)
(4,4)→( 4(1/2), 4(1/2)) =N (2,2)
Side of square ABCD is find out by distance formula i.e., d= √square of difference of x-coordinates + square of difference of y-coordinates
Length of AB = √ 0+4 = 2unit
Perimeter of Square of ABCD = 8 units
area of Square ABCD = 4 square units
Length of KL = √0+2 = √2 units
Perimeter of Square KLMN= 4√2 units
Area of Square KLMN= 2 square units
Ratio of ( new to original) of perimeter = 4√2/8 = 1/√2
Ratio of ( new to original) of area = 2/4 = 1/2
To learn more about dilation , refer :
https://brainly.com/question/3123885
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